Question

the measure of arc qs is (4x - 18)°. what is the value of x? 40.5 49.5 94.5 180

Explanation:

Step1: Identify the arc type

Since \(\angle QRS\) is a right angle (\(90^\circ\)) and \(QS\) is a diameter (as \(T\) is the center), arc \(QS\) is a semicircle, so its measure is \(180^\circ\).

Step2: Set up the equation

We know arc \(QS=(4x - 18)^\circ\) and arc \(QS = 180^\circ\), so:
\(4x-18 = 180\)

Step3: Solve for \(x\)

Add 18 to both sides:
\(4x=180 + 18=198\)
Divide both sides by 4:
\(x=\frac{198}{4}=49.5\)

Answer:

\(x = 49.5\) (corresponding to the option 49.5)